LDA on Social Bookmarking Systems: an experiment on CiteUlike

Introduction to Natural Language Processing, CS2731 Professor Rebecca Hwa University of Pittsburgh Denis Parra-Santander December 16th 2009

1

Outline

2

Outline

Topic Modeling Joke (check mood of people…)

LDA Introduction

Sorry I’m nervous…

Motivation Smart

Statement…

Definitions

Monte Carlo: a great place pass your vacations

DIRICHLET: [diʀiˈkleː]

Uuuh…

Uuuh…

Experiments

Results

END

Evaluation method

Topic modeling: Evolution LSA [Deerwester et al. 90]: find “latent”

structure or “concepts” in a text corpus.: ◦ Compare texts using a vector-based

representation that is learned from a corpus. Relies on SVD (for dimensionality reduction)

PLSA [Hoffman 99] extends LSA by adding the idea of mixture decomposition derived from a latent class model.

LDA [Blei et al. 2004] : extends PLSA by using a generative model, in particular, by adding a Dirichlet prior.

3

Document 22

LDA : Generative Model* (I/II)

4

Words: Information About catalog pricing changes 2009 welcome looking hands-on science ideas try kitchen

• LDA assumes that each word in the document was generated by a distribution of topics over words.

Topic 15: science experiment learning ideas practice information

Topic 9: catalog shopping buy internet checkout cart

• Paired with an inference mechanism (Gibbs sampling), learns per-document distribution over topics, per-topic distributions over words

…

*Original slide by Daniel Ramage, Stanford University

LDA I/II : Graphical Model

5

Graphical model representations

Compact notation:

Cat

w1 w2 w3 w4 wn …

*Original slide by Roger Levy, UCSD

Cat

w1 n

“generate a word from Cat n times” a “plate”

LDA II/II : Graphical Model

6

Nd D

zi

wi

θ (d)

φ (j)

α

β θ (d) ∼ Dirichlet(α)

zi ∼ Discrete(θ (d) ) φ (j) ∼ Dirichlet(β)

wi ∼ Discrete(φ (zi) )

T

distribution over topics for each document

topic assignment for each word

distribution over words for each topic

word generated from assigned topic

Dirichlet priors

*Original slide by Roger Levy, UCSD

Learning the parameters

7

Maximum likelihood estimation (EM) ◦ e.g. Hofmann (1999)

Deterministic approximate algorithms ◦ variational EM; Blei, Ng & Jordan (2001; 2003) ◦ expectation propagation; Minka & Lafferty

(2002) Markov chain Monte Carlo ◦ full Gibbs sampler; Pritchard et al. (2000) ◦ collapsed Gibbs sampler; Griffiths & Steyvers

(2004)

*Original slide by Roger Levy, UCSD

My Experiments Identify Topics in a collection of documents

from a social bookmarking system (citeULike) [Ramage et al. 2008]

Objective: Clusterise documents by LDA QUESTION: If the documents have, in

addition to title and text, USER TAGS… how can they help/influence/improve topic identification/clustering?

8

Tools available

Many implementations of LDA based on Gibbs sampling:

LingPipe (Java) Mallet (Java) STMT (Scala) – I chose this one

9

The Dataset Initially ◦ Corpus: ~45k documents, ◦ Definition of 99 topics (queries) ◦ Gold-std : Identification document-topic by

expert feedback, defining a ground-truth But then, then gold-standard and RAM… ◦ Not all documents were relevant ◦ Unable to train model with 45k, 20k and10k

And then, the tags: not all the documents in gold-standard had associated tags (#>2) ◦ Finally: Training with 1.1k documents ◦ Experiments on 212 documents

10

Evaluation: Pair-wise precision / recall

11

*Original slide by Daniel Ramage, Stanford University

… results …

12

Perplexity

13

# of topics

38 52 99

Content Tags 1860.7642 1880.7974 1270.8032

Title + text

2526.7589 2447.5477 2755.1329

Using Stanford Topic Modeling Toolbox (STMT) Training with ~1.1k documents, 80% training, 20% to calculate pp.

F1 ( & precision/recall)

F-1, in parenthesis precision and recall

14

# of topics

38 52 99

Tags 0.139 (0.118/0.167)

0.168 (0.187/0.152)

0.215 (0.267/0.18)

Title + text

0.1252 (0.122/0.128)

0.157 (0.151/0.163)

0.156 (0.198/0.129)

Conclusions Results are not the same than “motivational”

paper, though are consistent with their conclusions (dataset is very domain-specific)

Pending: combining tags and documents, in particular MM-LDA

Importance to NLP: extensions of the model have been used to: ◦ learn syntactic and semantic factors that guide

word choice ◦ Identify authorship ◦ Many others ()

15

… and to finish … Thanks! And…

16

“Invent new worlds and watch your word;

The adjective, when it doesn’t give life, kills…”

Ars Poetica Vicente Huidobro

“Inventa nuevos mundos y cuida tu palabra; El adjetivo, cuando no da vida, mata…”

17

References Heinrich, G. (2008). Parameter estimation for text analysis,. Technical report,

University of Leipzig.

Ramage, D., P. Heymann, C. D. Manning, and H. G. Molina (2009). Clustering the tagged web. In WSDM '09: Proceedings of the Second ACM International Conference on Web Search and Data Mining, New York, NY, USA, pp. 54-63. ACM.

Steyvers, M. and T. Griffiths (2007). Probabilistic Topic Models. Lawrence Erlbaum Associates.

18

Backup Slides

19

LSA: 3 claims (2 match with LDA)

Semantic Information can be derived from a word-document co-ocurrence matrix

Dimensionality reduction is an essential part of this derivation

Words and documents can be represented as points in an Euclidean Space => different than LDA: semantic properties of words and docs are expressed in terms of probabilistic topics

20

21

Parameter estimation and Gibbs Sampling (3 Slides)

Inverting the generative model

Maximum likelihood estimation (EM) ◦ e.g. Hofmann (1999)

Deterministic approximate algorithms ◦ variational EM; Blei, Ng & Jordan (2001; 2003) ◦ expectation propagation; Minka & Lafferty (2002)

Markov chain Monte Carlo ◦ full Gibbs sampler; Pritchard et al. (2000) ◦ collapsed Gibbs sampler; Griffiths & Steyvers (2004)

The collapsed Gibbs sampler

Using conjugacy of Dirichlet and multinomial distributions, integrate out continuous parameters

Defines a distribution on discrete ensembles z

ΦΦΦ= ∫∆

dpPPTW

)(),|()|( zwzw

ΘΘΘ= ∫∆

dpPPDT

)()|()( zz

∑=

zzzw

zzwwz)()|(

)()|()|(PP

PPP

∏ ∑∏

= +ΓΓ

Γ

+Γ=

T

jw

jw

Ww

jw

nWn

1)(

)(

)()(

)()(

ββ

ββ

∏ ∑∏

= +ΓΓ

Γ

+Γ=

D

dj

dj

Tj

dj

nTn

1)(

)(

)()(

)(

)(

αα

α

α

The collapsed Gibbs sampler

Sample each zi conditioned on z-i

This is nicer than your average Gibbs sampler: ◦ memory: counts can be cached in two sparse matrices ◦ optimization: no special functions, simple arithmetic ◦ the distributions on Φ and Θ are analytic given z and w, and can

later be found for each sample

αα

ββ

Tnn

Wnn

zPi

i

i

i

i

d

dj

z

zw

ii +

+

+

+∝

••− )(

)(

)(

)(

),|( zw

Gibbs Sampling from PTM paper

25

26

Extensions and Applications

Nu U

zi

wi

θ(u)

φ (j)

α

β

θ(u)|su=0 ∼ Delta(θ(u-1)) θ(u)|su=1 ∼ Dirichlet(α)

zi ∼ Discrete(θ (u) )

φ (j) ∼ Dirichlet(β)

wi ∼ Discrete(φ (zi) )

T

Extension: a model for meetings

su

θ(u-1) …

(Purver, Kording, Griffiths, & Tenenbaum, 2006)

Sample of ICSI meeting corpus (25 meetings)

no it's o_k. it's it'll work. well i can do that. but then i have to end the presentation in the middle so i can go back to open up javabayes. o_k fine. here let's see if i can. alright. very nice. is that better. yeah. o_k. uh i'll also get rid of this click to add notes. o_k. perfect NEW TOPIC (not supplied to algorithm) so then the features we decided or we decided we were talked about. right. uh the the prosody the discourse verb choice. you know we had a list of things like to go and to visit and what not. the landmark-iness of uh. i knew you'd like that. nice coinage

Topic segmentation applied to meetings

Inferred Segmentation

Inferred Topics

Comparison with human judgments

Topics recovered are much more coherent than those found using random segmentation, no segmentation, or an HMM

Learning the number of topics

Can use standard Bayes factor methods to evaluate models of different dimensionality ◦ e.g. importance sampling via MCMC

Alternative: nonparametric Bayes ◦ fixed number of topics per document,

unbounded number of topics per corpus (Blei, Griffiths, Jordan, & Tenenbaum, 2004)

◦ unbounded number of topics for both (the hierarchical Dirichlet process)

(Teh, Jordan, Beal, & Blei, 2004)

The Author-Topic model (Rosen-Zvi, Griffiths, Smyth, & Steyvers, 2004)

Nd D

zi

wi

θ (a)

φ (j)

α

β

θ (a) ∼ Dirichlet(α)

zi ∼ Discrete(θ (xi) ) φ (j) ∼ Dirichlet(β)

wi ∼ Discrete(φ (zi) )

T

xi

A

xi ∼ Uniform(A (d) )

each author has a distribution over topics

the author of each word is chosen uniformly at random

Four example topics from NIPS

WORD PROB. WORD PROB. WORD PROB. WORD PROB.LIKELIHOOD 0.0539 RECOGNITION 0.0400 REINFORCEMENT 0.0411 KERNEL 0.0683

MIXTURE 0.0509 CHARACTER 0.0336 POLICY 0.0371 SUPPORT 0.0377

EM 0.0470 CHARACTERS 0.0250 ACTION 0.0332 VECTOR 0.0257

DENSITY 0.0398 TANGENT 0.0241 OPTIMAL 0.0208 KERNELS 0.0217GAUSSIAN 0.0349 HANDWRITTEN 0.0169 ACTIONS 0.0208 SET 0.0205

ESTIMATION 0.0314 DIGITS 0.0159 FUNCTION 0.0178 SVM 0.0204

LOG 0.0263 IMAGE 0.0157 REWARD 0.0165 SPACE 0.0188

MAXIMUM 0.0254 DISTANCE 0.0153 SUTTON 0.0164 MACHINES 0.0168PARAMETERS 0.0209 DIGIT 0.0149 AGENT 0.0136 REGRESSION 0.0155

ESTIMATE 0.0204 HAND 0.0126 DECISION 0.0118 MARGIN 0.0151

AUTHOR PROB. AUTHOR PROB. AUTHOR PROB. AUTHOR PROB.Tresp_V 0.0333 Simard_P 0.0694 Singh_S 0.1412 Smola_A 0.1033

Singer_Y 0.0281 Martin_G 0.0394 Barto_A 0.0471 Scholkopf_B 0.0730

Jebara_T 0.0207 LeCun_Y 0.0359 Sutton_R 0.0430 Burges_C 0.0489Ghahramani_Z 0.0196 Denker_J 0.0278 Dayan_P 0.0324 Vapnik_V 0.0431

Ueda_N 0.0170 Henderson_D 0.0256 Parr_R 0.0314 Chapelle_O 0.0210

Jordan_M 0.0150 Revow_M 0.0229 Dietterich_T 0.0231 Cristianini_N 0.0185Roweis_S 0.0123 Platt_J 0.0226 Tsitsiklis_J 0.0194 Ratsch_G 0.0172

Schuster_M 0.0104 Keeler_J 0.0192 Randlov_J 0.0167 Laskov_P 0.0169

Xu_L 0.0098 Rashid_M 0.0182 Bradtke_S 0.0161 Tipping_M 0.0153

Saul_L 0.0094 Sackinger_E 0.0132 Schwartz_A 0.0142 Sollich_P 0.0141

TOPIC 19 TOPIC 24 TOPIC 29 TOPIC 87

Who wrote what?

A method1 is described which like the kernel1 trick1 in support1 vector1 machines1 SVMs1 lets us generalize distance1 based2 algorithms to operate in feature1 spaces usually nonlinearly related to the input1 space This is done by identifying a class of kernels1 which can be represented as norm1 based2 distances1 in Hilbert spaces It turns1 out that common kernel1 algorithms such as SVMs1 and kernel1 PCA1 are actually really distance1 based2 algorithms and can be run2 with that class of kernels1 too As well as providing1 a useful new insight1 into how these algorithms work the present2 work can form the basis1 for conceiving new algorithms

This paper presents2 a comprehensive approach for model2 based2 diagnosis2 which includes proposals for characterizing and computing2 preferred2 diagnoses2 assuming that the system2 description2 is augmented with a system2 structure2 a directed2 graph2 explicating the interconnections between system2 components2 Specifically we first introduce the notion of a consequence2 which is a syntactically2 unconstrained propositional2 sentence2 that characterizes all consistency2 based2 diagnoses2 and show2 that standard2 characterizations of diagnoses2 such as minimal conflicts1 correspond to syntactic2 variations1 on a consequence2 Second we propose a new syntactic2 variation on the consequence2 known as negation2 normal form NNF and discuss its merits compared to standard variations Third we introduce a basic algorithm2 for computing consequences in NNF given a structured system2 description We show that if the system2 structure2 does not contain cycles2 then there is always a linear size2 consequence2 in NNF which can be computed in linear time2 For arbitrary1 system2 structures2 we show a precise connection between the complexity2 of computing2 consequences and the topology of the underlying system2 structure2 Finally we present2 an algorithm2 that enumerates2 the preferred2 diagnoses2 characterized by a consequence2 The algorithm2 is shown1 to take linear time2 in the size2 of the consequence2 if the preference criterion1 satisfies some general conditions

Written by (1) Scholkopf_B

Written by (2) Darwiche_A

Analysis of PNAS abstracts

Test topic models with a real database of scientific papers from PNAS

All 28,154 abstracts from 1991-2001 All words occurring in at least five

abstracts, not on “stop” list (20,551) Total of 3,026,970 tokens in corpus

(Griffiths & Steyvers, 2004)

FORCE SURFACE

MOLECULES SOLUTION SURFACES

MICROSCOPY WATER

FORCES PARTICLES STRENGTH POLYMER

IONIC ATOMIC

AQUEOUS MOLECULAR PROPERTIES

LIQUID SOLUTIONS

BEADS MECHANICAL

HIV VIRUS

INFECTED IMMUNODEFICIENCY

CD4 INFECTION

HUMAN VIRAL TAT

GP120 REPLICATION

TYPE ENVELOPE

AIDS REV

BLOOD CCR5

INDIVIDUALS ENV

PERIPHERAL

MUSCLE CARDIAC HEART

SKELETAL MYOCYTES

VENTRICULAR MUSCLES SMOOTH

HYPERTROPHY DYSTROPHIN

HEARTS CONTRACTION

FIBERS FUNCTION

TISSUE RAT

MYOCARDIAL ISOLATED

MYOD FAILURE

STRUCTURE ANGSTROM

CRYSTAL RESIDUES

STRUCTURES STRUCTURAL RESOLUTION

HELIX THREE

HELICES DETERMINED

RAY CONFORMATION

HELICAL HYDROPHOBIC

SIDE DIMENSIONAL

INTERACTIONS MOLECULE SURFACE

NEURONS BRAIN

CORTEX CORTICAL

OLFACTORY NUCLEUS

NEURONAL LAYER

RAT NUCLEI

CEREBELLUM CEREBELLAR

LATERAL CEREBRAL

LAYERS GRANULE LABELED

HIPPOCAMPUS AREAS

THALAMIC

A selection of topics

TUMOR CANCER TUMORS HUMAN CELLS

BREAST MELANOMA GROWTH

CARCINOMA PROSTATE NORMAL

CELL METASTATIC MALIGNANT

LUNG CANCERS

MICE NUDE

PRIMARY OVARIAN

Cold topics Hot topics

2 SPECIES GLOBAL CLIMATE

CO2 WATER

ENVIRONMENTAL YEARS MARINE CARBON

DIVERSITY OCEAN

EXTINCTION TERRESTRIAL COMMUNITY ABUNDANCE

134 MICE

DEFICIENT NORMAL

GENE NULL

MOUSE TYPE

HOMOZYGOUS ROLE

KNOCKOUT DEVELOPMENT

GENERATED LACKING ANIMALS

REDUCED

179 APOPTOSIS

DEATH CELL

INDUCED BCL

CELLS APOPTOTIC

CASPASE FAS

SURVIVAL PROGRAMMED

MEDIATED INDUCTION CERAMIDE

EXPRESSION

37 CDNA AMINO

SEQUENCE ACID

PROTEIN ISOLATED ENCODING

CLONED ACIDS

IDENTITY CLONE

EXPRESSED ENCODES

RAT HOMOLOGY

289 KDA

PROTEIN PURIFIED

MOLECULAR MASS

CHROMATOGRAPHY POLYPEPTIDE

GEL SDS

BAND APPARENT LABELED

IDENTIFIED FRACTION DETECTED

75 ANTIBODY

ANTIBODIES MONOCLONAL

ANTIGEN IGG MAB

SPECIFIC EPITOPE HUMAN MABS

RECOGNIZED SERA

EPITOPES DIRECTED

NEUTRALIZING

38

The effect of Alpha and beta as hyperparameters

Effects of hyperparameters

α and β control the relative sparsity of Φ and Θ ◦ smaller α, fewer topics per document ◦ smaller β, fewer words per topic

Good assignments z compromise in sparsity

log

Γ(x)

x

∏ ∑∏

= +ΓΓ

Γ

+Γ=

T

jw

jw

Ww

jw

nWn

P1

)(

)(

)()(

)()(

)|(β

ββ

βzw

∏ ∑∏

= +ΓΓ

Γ

+Γ=

D

dj

dj

Tj

dj

nTn

P1

)(

)(

)()(

)(

)()(

αα

α

αz

Varying α

decreasing α increases sparsity

Varying β decreasing β

increases sparsity ?

Multi-Multinomial LDA (MM-LDA)

42

Ramage 2009 results

43